Which books or papers clearly explain the relation between Ising models and deep neural networks?
The following articles


Ising models for networks of real neurons (2006) by Gasper Tkacik et al.
Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models (2018) by Kyle Mills et al.
Inverse Ising inference by combining Ornstein-Zernike theory with deep learning (2017) by Soma Turi, Alpha A. Lee et al.
Neural-network based general method for statistical mechanics on sparse systems (2019) by Feng Pan, Hai-Jun Zhou, Pan Zhang et al.


may help you understand the "relationship" between Ising models and DNN, assuming you know what the Ising model is and what a DNN is, the similarity should be fairly intuitive to you. 

The Ising model is a sort of floating soup of ferromagnetic particles each generating their own small magnetic field either working against or with their neighbor. When many of the particles aline, they create an aligned field we refer to as a dipole moment in magnetism, while in a DNN we refer to the joined effort of a few entities working to cause a larger effect in another entity an 'activation function'. In a fully connected DNN, where the Euclidean distance weights the connections and the nodes are initialized with a certain magnetic polarity in relation to the axis of the magnetic field it generates, the network would be an almost exact representation of the reality of what the Ising model seeks to simplify.